In this paper we introduce a novel algorithm of calculating arbitrary order cumulants of multidimensional data. Since the n order cumulant can be presented in the form of an n-dimensional tensor, the algorithm is presented using the tensor network notation. The presented algorithm exploits the super–symmetry of cumulant and moment tensors. We show, that proposed algorithm highly decreases the c...

We develop an entanglement criterion with third- and fourth-order cumulants to detect the of non-Gaussian states. The efficiency is investigated for gravitating mirrors in optomechanical systems. show that entangled regime enlarged by cumulants. also discuss limitations a highly state.

We describe an algorithm computing the exact value of the mean current, its variance, and higher order cumulants for stochastic driven systems. The method uses a Rayleigh-Schrödinger perturbation expansion of the generating function of the current, and can be extended to compute covariances of multiple currents. As an example of application of the method, we give numerical evidence for a simple...

For a discrete distribution in Rd on a finite support D probabilities and moments are algebraically related. If there are n = |D| support points then there are n probabilities p(x), x ∈ D and n basic moments. By suitable interpolation of the probabilities using a Gröbner basis method, high order moments can be express linearly in terms of n basic moments. A main result is that high order cumula...

This paper describes a non-linear deterministic estimator based on cumulants for the extraction of modal parameters. The signal analysed is composed of multiple exponentially damped real sinusoids in unknown additive noise. Cumulants reduce signiicantly the eeects of noise and are also an eecient way of compressing the sampled data. In modal analysis a sensor may be unable to detect some modes ...

In this paper, we introduce two new features for the design of electroencephalography (EEG) based Brain-Computer Interfaces (BCI): one feature based on multifractal cumulants, and one feature based on the predictive complexity of the EEG time series. The multifractal cumulants feature measures the signal regularity, while the predictive complexity measures the difficulty to predict the future o...

Abstra t. Let P be the set of all probability measures on R possessing moments of every order. Consider P as a semigroup with respe t to onvolution. After topologizing P in a natural way, we determine all ontinuous homomorphisms of P into the unit ir le and, as a orollary, those into the real line. The latter are pre isely the nite linear ombinations of umulants, and from these all the former a...